Відповіді на вправи: 469 (1-10)

1) x² + 3х – 18 > 0;

x₁ = –6, x₂ = 3;

x $\in$ (–$\infty$; –6) $\cup$ (3; +$\infty$).

2) x² – 3х – 10 < 0;

x² – 3х – 10 = 0;

x₁ = –2, x₂ = 5;

x $\in$ (–2; 5).

3) x² – 4x – 12 $\le$ 0;

x² – 4x – 12 = 0;

x₁ = –2, x₂ = 6;

x $\in$ [–2; 6].

4) –x² + 10x – 24 $\le$ 0 |• (–1);

x² – 10x + 24 $\ge$ 0;

x² – 10 + 24 = 0;

x₁ = 4, x₂ = 6;

x $\in$ (–$\infty$; 4] $\cup$ [6; +$\infty$).

5) –x² – 4x + 5 < 0 |• (–1);

x² + 4x – 5 > 0;

x² + 4x – 5 = 0;

x₁ = –5, x₂ = 1.

x $\in$ (–$\infty$; –5) $\cup$ (1; +$\infty$).

6) x² – 4x + 3 $\ge$ 0;

x² – 4x + 3 = 0;

x₁ = 1, x₂ = 3;

x $\in$ (–$\infty$; 1] $\cup$ [3; +$\infty$).

7) x² – 6x – 16 < 0;

x² – 6x – 16 = 0;

x₁ = –2, x₂ = 8.

x $\in$ (–2; 8).

8) x² + 10x + 16 > 0;

x² + 10x + 16 = 0;

x₁ = –8, x₂ = –2.

x $\in$ (–$\infty$; –8) $\cup$ (–2; +$\infty$).

9) x² + 8х – 9 < 0;

x² + 8х – 9 = 0;

x₁ = –9, x₂ = 1;

x $\in$ (–9; 1).

10) x² – 10x + 21 $\le$ 0;

x² – 10x + 21 = 0;

x₁ = 3, x₂ = 7;

x $\in$ [3; 7].

11) x² + 2x – 15 < 0;

x² + 2x – 15 = 0;

x₁ = –5, x₂ = 3;

x $\in$ (–5; 3).

12) x² – 6x – 7 $\ge$ 0;

x² – 6x – 7 = 0;

x₁ = –1, x₂ = 7;

x $\in$ (–$\infty$; –2] $\cup$ [7; +$\infty$).

13) x² + 4x – 12 $\le$ 0;

x² + 4x – 12 = 0;

x₁ = –6, x₂ = 2;

x $\in$ (–$\infty$; –2) $\cup$ (2; +$\infty$).

14) x² + 4x – 12 < 0;

x² + 4x – 12 = 0;

x₁ = –6, x₂ = 2;

x $\in$ (–$\infty$; –2) $\cup$ (2; +$\infty$).

15) x² + 5x + 6 $\ge$ 0;

x² + 5x + 6 = 0;

D < 0;

x $\in$ (–$\infty$; +$\infty$).

16) x² – 3х – 40 > 0;

x² – 3х – 40 = 0;

x₁ = –5, x₂ = 8;

x $\in$ (–$\infty$; –5) $\cup$ (8; +$\infty$).